Question: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 8x + 6$ and $ KL = 6x + 20$ Find $JL$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {8x + 6} = {6x + 20}$ Solve for $x$ $ 2x = 14$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 8({7}) + 6$ $ KL = 6({7}) + 20$ $ JK = 56 + 6$ $ KL = 42 + 20$ $ JK = 62$ $ KL = 62$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {62} + {62}$ $ JL = 124$